SOLUTION: In 1990, the population of Africa was 643 million and by 2000 it had grown to 813 million. a. Use the exponential growth model A=A0e^kt, in which t the number of years after 199

Question 1029620: In 1990, the population of Africa was 643 million and by 2000 it had grown to 813 million.
a. Use the exponential growth model A=A0e^kt, in which t the number of years after 1990, to find the exponential growth function that models the data.
b. By which year will Africa's population reach two billion?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In 1990, the population of Africa was 643 million and by 2000 it had grown to 813 million.
Points:: (0,643); (10,813)
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a. Use the exponential growth model A=Aoe^kt, in which t the number of years
after 1990, to find the exponential growth function that models the data.
813 = 643*e^(k*10)
e^(10k) = 1.2644
10k = ln(1.2644)
k = 0.02346
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Eq:: A(t) = 643*e^(0.02346t)
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b. By which year will Africa's population reach two billion?
Note:: 2 billion = 2000 million
2000 = 643*e^(0.02346t)
e^0.02346t = 3.11
0.02346t = ln(3.11) = 1.1346
t = 48.36 years
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Ans: 1990 + 48.36 years occurs in the year 2039
Cheers,
Stan H.
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